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RESEARCH PRODUCT

Statistics of return times for weighted maps of the interval

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For non markovian, piecewise monotonic maps of the interval associated to a potential, we prove that the law of the entrance time in a cylinder, when renormalized by the measure of the cylinder, converges to an exponential law for almost all cylinders. Thanks to this result, we prove that the fluctuations of Rn, first return time in a cylinder, are lognormal.